Carrier phase of a harmonically mode-locked optical frequency comb (OFC) is investigated in detail. While harmonically mode-locked OFCs show promise for high-repetition-rate applications, their mode spacing is not the same as the pulse repetition rate, unlike fundamentally mode-locked OFCs. Consequently, harmonically mode-locked OFCs are unsuitable for applications requiring OFCs with wide mode spacing. This study examines the pulse-to-pulse carrier phase evolution of 4th- and 5th-order harmonically mode-locked OFCs, revealing uneven carrier phase evolution responsible for the narrow mode spacing. The possibility of achieving harmonically mode-locked OFCs with wide mode spacing is suggested by implementing pulse-to-pulse phase modulation to ensure even phase evolution.